Police said the woman mistook the car for a taxi and boarded it on Sunday morning in the popular town of Manali to go to a neighbouring district.
She was allegedly taken to a secluded spot and raped there by two men.
Manali is a popular Himalayan destination among foreigners and domestic tourists.
The woman was trying to reunite with her friends in Keylong when she boarded the car, which was carrying six people, police said.
“Arresting the four men who are absconding is our topmost priority. We have alerted police in all nearby districts,” police superintendent Padam Chand said.
The woman is being treated in hospital.
Manali is frequented by foreigners due to its picturesque valleys, but the security of women remains a concern.
An American woman was raped in Manali in 2013 by three men when she boarded a truck.
Scrutiny of sexual violence in India has grown since the 2012 gang rape and murder of a student on a Delhi bus.
The 2012 incident led to protests and new anti-rape laws in India. However, brutal sexual attacks against women and children continue to be reported across the country.